Career Concerns And The Optimal Pay-for-Performance Sensitivity

Transcription

1 Career Concerns And The Optimal Pay-for-Performance Sensitivity Qi Chen and Wei Jiang This draft: February 2006 Abstract Prior literature suggests that managers career concerns provide implicit incentive mechanisms for their behaviors (Fama (1980), Holmstrom (1999)), and may substitute the explicit incentives in their compensation contracts (Gibbons and Murphy (1992)). We show that the substitution effect can be weakened, and even reversed, when managers perform multiple tasks and are concerned about both the level and variability of their reputation. We also find that after taking into consideration managers concerns for the variability of their reputation, the optimal pay-for-performance sensitivity can also be increasing in the underlying risk measure. We test these predictions using a large sample of chief executive officers compensations over ; results are consistent with our model predictions. (JEL: J31; J41; D80) The Fuqua School of Business, Duke University, Durham, NC 27708, qc2@duke.edu; Columbia Business School, New York, NY 10027, wj2006@columbia.edu. We received helpful comments from Jim Anton, Robert Bushman, Harry Evans, Jennifer Francis, Itay Goldstein, Thomas Hemmer, Steve Kaplan, Young Kwon, Tracy Lewis, Mike Riordan, and workshop participants at University of California Berkeley and HKUST. We are responsible for all remaining errors. The research was supported by the Fuqua School of Business, Duke University and the Eugene Lang Center of Entrepreneurialship, Columbia Business School. 1

2 Career Concerns and the Optimal Pay-for-Performance Sensitivity Abstract Prior literature suggests that managers career concerns provide implicit incentive mechanisms for their behaviors (Fama (1980), Holmstrom (1999)), and may substitute the explicit incentives in their compensation contracts (Gibbons and Murphy (1992)). We show that the substitution effect can be weakened, and even reversed, when managers perform multiple tasks and are concerned about both the level and variability of their reputation. We also find that after taking into consideration managers concerns for the variability of their reputation, the optimal pay-for-performance sensitivity can also be increasing in the underlying risk measure. We test these predictions using a large sample of chief executive officers compensations over ; results are consistent with our model predictions. (JEL: J31; J41; D80)

3 1 Introduction This paper examines the relation between managers career concerns and the optimal pay-forperformance sensitivities in their compensations. Corporate executives and managers are subject to various incentive mechanisms, including both explicit incentives from their compensation contracts, and implicit incentives from their career concerns, i.e., their concerns for their reputation in the external labor market. A central belief on the role of career concerns, as expressed in Fama (1980) and elaborated in Holmstrom (1999), is that they provide additional monitoring device, and therefore, may substitute explicit incentives. Gibbons and Murphy (1992) further formalize this substitutive relation by showing that in an optimal contract, a manager s pay-for-performance sensitivity (PPS, hereafter) should be lowered when his career concerns are stronger. However, researchers have also identified other effects of career concerns on managers behaviors, some of which are not to shareholders benefits. For example, theoretical works by Holmstrom and Ricart i Costa (1986) and Prendergast and Stole (1996) point out the negative effects of career concerns on agents behavior. Song and Thakor (2005) show that career concerns of CEOs, interacted with those of the board, distort investment selections and cause weakened governance. Chevalier and Ellison (1999) find empirical evidence that mutual fund managers career-concerns may distort their trading behaviors to the detriment of fund shareholders. These imply that career concerns may not be merely a solution to incentive problems, but can also be a source of incentive problems. As a result, the relation between explicit compensation contracts and managers career concerns may not be as straight-forward as the substitution effect suggested in prior literature. In this paper, we show that, indeed, the substitutive relation between implicit and explicit incentives can be weakened, and even reversed, depending on the nature of the manager s career concerns and thetypeoftasksheperforms. Specifically, we extend Gibbons and Murphy (1992) (GM, hereafter) along two dimensions. First, the manager in our model faces two types of career concerns: reputation concerns (as in GM), which refer to how the manager s current performance affects the level of his future compensation, and career-risk concerns, which refer to how the manager s current performance affects the variation in his future compensation. This extension is motivated by the fact that insurance markets for 1

4 human capital are likely incomplete (Holmstrom and Ricart i Costa (1986)). As a result, managers are often concerned about the risks associated with their future reputation and compensation. The second extension in our model is to introduce multiple tasks. In addition to the traditional production effort (as in GM), the manager in our model also exerts an information effort. Unlike production effort, information effort does not directly increase current or future output in the sense of first-order stochastic dominance. Instead, it produces more precise information about the firm s profitability (which is related to managerial talent), which benefits the firm. The multitask setting is more descriptive of corporate executives responsibilities. Managers, especially Chief Executive Officers (CEOs), are responsible for day-to-day operations, which correspond to production effort in our model. They also spend significant amount of time analyzing firms market positions, gathering information about investment opportunities or profitability, and setting future business strategy. These types of activities are captured by information effort in our model. Because these types of effort relate to firms future strategy, we use the term strategy effort interchangeably with information effort throughout the paper. We believe both extensions reflect more realistically the multi-dimensional aspects of corporate executives responsibilities and incentives (Holmstrom and Milgrom (1991), Milgrom and Roberts (1992)), and the important role that CEOs play in setting corporation strategies in addition to improving production (Dow and Raposo (2005)). The key insight from our model is that career concerns (more specifically, career-risk concerns) reduce a manager s incentive for strategy effort. The intuition is the following. While the information uncovered from the manager s strategy effort helps the firm make better decisions, it also reveals information about the manager s ability to succeed in the future. More strategy effort provides more precise information to reduce the firm s ex post uncertainty about the manager s ability (after the effort is exerted and the information revealed); at the same time, it increases the ex ante uncertainty about how the manager may be perceived by the labor market. 1 Such ex ante 1 The intuition is the following. For a given level of ex ante uncertainty in a parameter (such as managerial talent), the more precise a signal is, the more the updated assessment of the parameter (after incorporating the signal) deviates from its prior (and hence the more expected risk the manager faces). A more mathematical version of this intuition is in footnote 23. 2

5 uncertainty is costly to the manager because it increases the variability of his future compensation. As a result, the manager will under-supply strategy effort, more so when his career-risk concerns are stronger. We show that to overcome the negative effect of career-risk concerns on the manager s strategy effort, the firm may find it optimal to increase the manager s explicit pay-for-performance sensitivity; more so when managers career-risk concerns are higher. between PPS and career concerns established in prior literature. This weakens the negative relation Further, because the manager s career-risk concerns are higher when the underlying uncertainty about his ability is high, the firm may choose a higher PPS in riskier environment. This weakens the negative relation between PPS and project risk from the standard agency model (e.g., Holmstrom and Milgrom (1987)). 2 In summary, our model generates predictions not suggested by the existing literature. model predicts that both the relation between career concerns and PPS and that between risk and PPS are less negative, and may even turn positive, for firms that benefit more from strategy effort (such as firms with high growth potential), or firms where managers stakes in firms future wealth are small (such as large firms). These predictions are consistent with anecdotal evidence suggesting that strong implicit incentives and risky environments do not always suppress PPS. Our For example, managers in start-up firms, or newly appointed CEOs, often receive highly performance-sensitive compensations (such as restricted stocks or stock options), even though they have relatively strong career concerns. 3 Career concerns clearly provide implicit incentives to executives in the information technology (IT) industries, as evidenced by the high turnover rates for IT executives. At the same time, IT executives PPS are significantly higher than their counterparts in non-it firms (Anderson, Banker, and Ravindran (2000), Ittner, Lambert, and Larcker (2003), Murphy (2003)). Kaplan and Stromberg (2004) also find a positive relation between PPS for managers in start-up firms and some measures 2 Empirical support for the negative risk-incentive relation is mixed (see Demsetz and Lehn (1985), Jensen and Murphy (1990) and Aggarwal and Samwick (1999) for examples), and therefore, has prompted several authors to propose alternative explanations (e.g., Core and Qian (2001), Prendergast (2002), Hemmer (2002), Raith (2003), and Oyer and Schaefer (2005)). See also Chiappori and Salanie (2003) and Prendergast (2002) for recent surveys. 3 A Remix in the Grants of Options and Stock Special Report, The New York Times, April 6,

6 of external risk. 4 To the extent that strategy effort is important in these industries, our model offers an explanation for the above seemingly counter-intuitive facts. We test our model predictions using data on CEO compensation from the ExecuComp data base from We find that consistent with GM, CEO tenure and age (as inverse proxies for the strength of career concerns) are both positively correlated with PPS in CEO contracts. However, more relevant to our model predictions, we find that the relations are less positive for firms with higher growth potential and for larger firms. Similarly, we also find that while the average relation between PPS and firm risk is negative, they are less negative for large and high growth firms. These results are consistent with our model predictions. The SEC s decision in early 2006 to amend disclosure requirements for executive and director compensation reflects a growing attention from investors and regulators on executive pays. paper makes at least two contributions to the literature on executive compensation. Our First, it complements the theoretical literature on the relation between explicit and implicit incentives, and on the determinants of pay-for-performance sensitivity. In particular, we analyze how different types of implicit incentives jointly affect PPS. Our model endogenizes the information structure in the standard reputation concerns model. In our model compensation contracts affect the manager s information effort choice, which, in turn, affects the information available to the principal. paper differs from Meyer and Vickers (1997), Milbourn, Shockley, and Thakor (2001), Milbourn (2003), and Goel, Nanda, and Narayanan (2004) in that our manager performs multiple tasks that affect both the level and the variability of his expected future compensation. 5 Our Our paper shares a similar feature with Barron and Waddell (2003) in that the agent exerts non-contractible information effort. However, Barron and Waddell (2003) study a one-period model where the agent 4 Because these risk measures capture the external risk about which venture capitalists and managers are symmetrically informed, Kaplan and Stromberg (2004) conclude that this positive relation is hard to reconcile with a standard agency model (e.g., Holmstrom and Milgrom (1987)) or an information asymmetry explanation (e.g., Prendergast (2002)). In our model, the principal and the agent have incomplete but symmetric information about the underlying project profitability. 5 Dewatripont, Jewitt, and Tirole (1999) also study career concerns with multiple tasks. But their multiple tasks are of the same nature (i.e., they all affect current-period output in the first-order stochastic dominance manner). Further, they do not consider explicit contracts. 4

7 exerts only information effort and privately observes the outcome from this effort. In contrast, we analyze a dynamic model where the outcome of the agent s effort is observed by both the agent and the principal. The observability of the outcome of the agent s effort exacerbates the agent s career-risk concerns. Our paper also adds to the empirical literature on cross-sectional pay-for-performance heterogeneity in executive compensations. 6 We find large-sample evidence supporting the intuitive result from Fama (1980) that external labor market monitoring partially substitutes for explicit incentive compensation. More importantly, we document that the degree of this substitution varies with firm and executive characteristics. Further, to the best of our knowledge, our finding is the first to identify a link between implicit incentives and the much debated risk-incentive relation. The rest of the paper is organized as follows. Section 2 sets up the model and provides a lemma that facilitates solving the model. Section 3 solves the model. Section 4 discusses the testable hypotheses and presents supporting empirical results. Section 5 concludes. 2 Model set-up Our model set-up builds on that in Gibbons and Murphy (1992). In setting up the model, we start with the basic production function and the interpretation of the career-concerns parameter. We then introduce multitask and career-risk concerns. We next describe the contract form and the principal s constraints. We conclude the section by proving a lemma that would facilitate solving the model. 2.1 Basic production function and career concerns parameter A risk-neutral principal hires a risk- and effort-averse agent to manage a project that yields stochastic outputs in two periods. In each period t (t =1, 2), output y t is generated as the sum of 6 Gibbons (1998), Prendergast (1999), and Murphy (1999), among others, provide recent surveys of the literature. 5

8 the agent s nonnegative costly effort (e t ), a productivity measure (π t ), and random noise (ε t ): y 1 = π 1 + e 1 + ε 1, (1a) y 2 k = π 2 + e 2 + ε 2. (1b) The noise terms ε t (t =1, 2) are assumed to be distributed normal N(0, 1/p ε ), 7 mutually independent, and independent of π t. The coefficient k in (1b) measures the scale of production in the second period relative to the first period and captures the firm s (exogenous) growth potential. In a multiple-period context, y 2 can be viewed as the sum of outputs from all future periods. The project s profitability π t is an exogenous random variable that correlates over time through the following AR(1) system: π 1 = θ, (2a) π 2 = ρθ + p 1 ρ 2 = ρπ 1 + p 1 ρ 2, (2b) where θ is the part of the agent s ability or talent that persists over time. As is standard in the literature, we assume that the principal and the agent do not observe the true θ, but share the common prior that θ is distributed normal N(0, 1/p θ ). 8 Normalizing the mean of θ to zero is without loss of generality as we can view the value of θ as its deviation from the unconditional mean. In equation (2b), is a zero-mean normal innovation term in the second period s profitability (π 2 ) and is independent of π 1. We normalize the variance of tobethesameasthatofθ. This way, π 1 and π 2 have the same total unconditional variance for all values of ρ. As will be clear later, both ρ and the total ex ante uncertainty about π t affect the agent s incentives. This normalization allows us to isolate the effect of ρ, our measure of the intensity of the agent s career concerns, as discussed next. 7 Throughout the paper, σ 2 x denotes the variance of a random variable x, andp x 1/σ 2 x denotes the inverse of the variance (i.e., the precision). 8 An intuitive interpretation from Prendergast and Topel (1996) is that θ measures the fit between the agent and his job, and therefore is unknown to both the principal and the agent at the beginning of the project. In the example in the introduction section, θ measures the manager s ability to succeed in the foreign market. Laffont and Tirole (1988) and Lewis and Sappington (1997), among others, discuss the optimal contract when the agent has pre-contracting private information about θ. 6

9 The parameter ρ [0, 1] in equations (2a) and (2b) measures the project profitability persistence that is due to the persistence in the agent s ability. 9 It is interpreted as our measure for the intensity of the agent s career concerns, for two main reasons. First, ρ captures the sensitivity of the agent s future compensation to current performance. Both current and potential employers will rely on the first-period signals to update their assessment of the agent s value in the second period. higher the value of ρ is, the more the employers rely on first-period signals to assess the agent s ability. Thus, higher ρ implies higher sensitivity of the agent s future compensation to currentperiod performance. As a comparison, most studies on career concerns, such as GM, Holmstrom (1999), and Meyer and Vickers (1997), assume ρ to be one, which is a special case in our set-up. As equations (2a) and (2b) indicate, future profitability replicates current profitability without any innovation when ρ =1. As a result, the agent s future compensation is very sensitive to his current performance. In the other extreme when ρ =0, current performance is not at all informative about future productivity, in which case the agent has no career concerns and the dynamic contracting is reduced to a repeated single-period contracting. We allow ρ to vary between 0 and 1 to facilitate our analysis of how the explicit pay-for-performance sensitivity varies with the degree of the agent s career concerns. The second reason is that ρ captures the tenure effect. Recall that we model the second period as a reduced-form representation of all future periods. with the agent s expected tenure on the job. The Thus ρ is likely to correlate positively A shorter expected remaining tenure implies a lower correlation between the agent s ability and the firm s future productivity. 10 This point is subtle but important as both age and tenure on the job are standard (inverse) proxies for the intensity of 9 More realistically, firm profitability also depends on factors other than managerial ability. Adding factors to the profitability that are orthogonal to θ does not affect the results. 10 To see this point, consider the extreme case when the current manager is replaced after only one period and a new manager is randomly re-drawn from the population of managerial talent with the same unconditional distribution N(0, 1/p θ ). The distribution of the firm s profitability will then be re-set and will not be correlated with the distribution if the manager is not replaced. In this case, the current manager s remaining tenure is zero and so is the correlation between the firm s current and future profitability. Similar logic implies that the longer the current manager s expected tenure, the higher the correlation between the firm s current and future profitability. See Milbourn (2003) for an elaboration on this point. 7

10 career concerns in empirical studies. 2.2 Multitask and career-risk concerns A novel feature of our model is to recognize that managers tasks often involve activities that do not increase the firm s current output. Rather, these activities relate to the strategic aspects of the firm s operations and have implications for the firm s future operations. For example, executives often spend time gathering and analyzing information, investigating market conditions, and/or assessing the firm s growth potential in foreign markets. To model this aspect of managerial activities, we assume that in the first period, the agent can exert another non-contractible effort, a [0, 1], to produce a publicly verifiable report, s, about the project s profitability (π 1 ). We represent the report s as a noisy signal generated according to s = π 1 + η, where η is a normal noise term independent of π 1 with mean zero and precision 1 a a p θ. This particular functional form for the precision of η is for tractability and without loss of generality. It implies that higher a increases the precision of η, hence the informativeness of s about π 1. In the extremecaseofa =1, observing s is equivalent to observing π 1. Because π 1 and π 2 are correlated via managerial ability θ, s is informative about the manager s potential to succeed in the future. 11 To differentiate the agent s efforts, throughout the paper, we refer to a as information effort or strategy effort and e t (t =1, 2) in (1a) and (1b) as production effort. Our main model assumes that the principal uses the signal s for contracting purposes only. In the sensitivity analysis section, we show that introducing additional benefits of s does not affect our predictions. To introduce career-risk concerns, we assume that the agent does not have access to a perfect credit market. This assumption is consistent with empirical evidence suggesting that managers cannot perfectly hedge future career risks, especially early in their career (see, e.g., Jin (2002), Garvey and Milbourn (2003)). We assume that the agent s total utility is time additive. 12 The 11 Relatedtofootnote9,ourresultsdonotchangeifs is a signal of both managerial talent and other unrelated determinants of profitability. The key is that s is informative about θ. 12 That is, the agent s total lifetime utility is U = P T =2 t=1 U (ct), wherect is his consumption in period t. The 8

11 assumption is made for simplicity and is stronger than needed as it implies that the agent cannot insure against any of his future incomes. agent s reputation or human capital risk. All we need is some insurance incompleteness for the For tractability, we assume a mean-variance utility function for the agent s per-period utility. Thus, the agent s total expected utility at the beginning of the first period is: U(w t ; e t,a)= h E 0 (w 1 ) c(e 1 ) g (a) r i h 2 Var 0 (w 1 ) + E 0 (w 2 ) c(e 2 ) r i 2 Var 0 (w 2 ), (3) where w t (t =1, 2) is the agent s salary in period t, r measures the degree of the agent s risk aversion, and c(e t ) and g(a) are the costs of production and information effort respectively in monetary terms. For simplicity, we assume that c(e t ) is quadratic in e t with c(e t )= 1 2 e2 t, and g(a) is convex in a with g(0) = g 0 (0) = 0 and g 0 (1) =. Throughout the paper, E 0 ( ) and Var 0 ( ) represent ex ante (at the beginning of the first period) expectation and variance. 2.3 Contract form and constraints As in the standard career concerns models, we make two assumptions about feasible contracts. First, only one-period contracts are enforceable, that is, neither party can commit to ignoring information revealed after the first period. 13 Second, in each period t, the contract takes the linear form of w t = α t + β t y t + λ t s for some constants α t,β t, and λ t. 14 Signal s enters the contract because it can help the principal filter the output randomness unrelated to the agent s production effort. Lack of committed long-term contracts implies that α 2,β 2, and λ 2 can be functions of y 1 and s. Given the assumptions, it is instructive and without loss of generality to write the contracts ³ ct PT =2 t=1 alternative is U = U (as in GM) which assumes that a perfect credit market exists for hedging the agent s future income risks. 13 See Gibbons and Murphy (1992) and Meyer and Vickers (1997) for discussions on the equivalence of the optimal sequence of one-period contracts and the optimal renegotiation-proof long-term contract. In general, if full commitment is allowed, career concerns can be perfectly insured ex ante and would be a moot issue. 14 Holmstrom and Milgrom (1987) show that linear contracts are a reasonable approximation in the context of CARA utility and normal distributions. See Sung (1995), Ou-Yang (2003), and Hemmer (2002) for related discussions on this approximation. We focus on linear contracts because our primary interest is the relation between pay-for-performance and career concerns (as opposed to the optimal shape of the contract). 9

12 as w 1 = α 1 + β 1 (y 1 δs), (4a) w 2 = α 2 (s, y 1 )+β 2 (s, y 1 ) y 2, (4b) where δ = λ 1 /β 1,andbothα 2 and β 2 are linear functions of y 1 and s. 15 In setting the contracts, the principal observes three types of constraints. The first is the incentive compatibility constraint which states that the agent will choose e t and a to maximize his expected utility for any given contract. The second is the time consistency constraint which states that, at the start of period two, the principal will use the information gained from period one to set the period two contract. which we discuss next. The third is the agent s participation constraints for both periods, Participation constraint ensures that the agent s expected utility from entering the contract is as least as much as his best outside option at the time of the contract (denoted U t ). The agent s outside option value at the beginning of period one (U 1 ) is exogenous and is normalized to zero. The agent s period two reservation utility (U 2 ) is endogenous and depends on the information revealed from period one. If the period one information reflects favorably on his ability, the manager s outside option value (and hence his reservation level) will rise. Following Meyer and Vickers (1997), we assume that U 2 is proportional to the expected total surplus in period two. That is, U 2 = b TS 2 where TS 2 is the expected second-period output net of the agent s effort and risk-premium cost and b (0, 1) measures the agent s share. 16 A positive b is necessary for career concerns to affect the agent s behavior in period one. Most prior studies assume b =1, which is equivalent to assuming perfectly competitive and risk neutral firms with identical technologies. Allowing b to vary between 0 and 1 is a more general assumption. b can be interpreted as the bargaining power of the agent vis-a-vis the principal. As long as both 15 These are the standard results with normal distributions and linear contracts. See Meyer and Vickers (1997) for examples and detailed derivations. 16 The alternative specification is that the manager s outside opportunity is only proportional to his perceived ability, but not to the second-period pure contracting surplus. results. This specification does not change the qualitative 10

13 the principal and the agent are better off continuing the relationship than discontinuing it, any Nash-bargaining would result in a strict interior split of the total surplus, i.e., 0 <b<1. 17 The agent s bargaining power can come from his ability to threaten to take the project (and the surplus) to another principal. Carrying out such a threat is not without cost, e.g., the cost of job searching and relocation, and the cost of losing firm-specific human capital. The parameter b can also be affected by the firm s cost to replace the manager. It is crucial to our model that the agent captures some, but not all, of the surplus attributable to his ability. We conclude the set-up by summarizing the timeline in Figure 1: t =0 0 <t<1 t =1 1 <t<2 t =2 -? 1st-period contract signed (i.e., wage payment contingent on y 1 and s agreed). The agent chooses both e 1 and a efforts.? y 1 and s observed; 1st-period contract executed; and 2nd-period contract signed. The agent chooses e 2 effort.? y 2 observed and 2nd-period contract executed. Figure 1: Timeline 2.4 Contract on signal s Since π t is exogenously determined, the optimal performance metric should be the output filtered out, as much as possible, of the influence of π t. If the precision of s is exogenously given, Myers and Vickers (1997) show that the optimal weight on s, δ in (4a), should be set at δ = a. However, in our model the precision of s is affected by the agent s information effort a, which is not contractible. Further, the contract is offered to the agent before he chooses a. Thus, the weight on s cannot 17 In its simplest form, Nash bargaining maximizes the product of the two parties gains over their respective outside opportunities. Any interior split of rent (b (0, 1)) yields a positive product, which dominates a corner allocation (b = {0, 1}) where the value of the product is zero. This feature is preserved under generalized Nash bargainings. 11

14 directly depend on the actual a. We show next that a mechanism exists for the principal to contract on s in the first-period and achieve the same outcome as when a is contractible. Consider a one-period game for the moment. The principal offers the agent the following contract: w 1 = α 1 + β 1 (y 1 eas), (5) where ea is the agent s announcement of his a effort made after he chooses a but before s is realized, and α 1 and β 1 are constants independent of ea. The following Lemma shows that it is always in the agent s best interest to announce the true a, even when he is not constrained to tell the truth. The proof is in the Appendix (A1). Lemma 1 Suppose the principal offers the agent a wage schedule in the form of (5). In a oneperiod model, given any α 1 and β 1, ea = a is an equilibrium outcome. Lemma 1 implies that an optimal contract can be contingent on s in a one-period model, even when the precision of s is not contractible. In the two-period set-up, a necessary condition for Lemma 1 to hold is that the announced ea is used only in the form of (5). For example, the principal cannot use the announcement to punish the agent for not choosing the principal s desired a. 18 assume that a is observable but not contractible. 19 We Under such circumstances, both the principal and the labor market will use the observed a to determine the second-period compensation for the agent and use the announced ea only for the first-period contract (and in equilibrium the agent will announce truthfully). This assumption isolates the role of explicit incentives in motivating information effort from their role of extracting information from the agent. the symmetric information structure of our model. It also maintains In the sensitivity analysis section, we show 18 In general, the agent s choice of a is not necessarily the same as what principal would have chosen had a been contractible. Corollary 1 in Sung (1995) provides conditions under which the principal and the agent would choose the same a. It is easy to verify that those conditions are satisfied in the one-period version of our model (where ρ =0), but not in a dynamic setting where the second-period incentives depend on the first-period information. 19 Aghion and Bolton (1992) offer a theoretical analysis on observable but not verifiable situations in financial contracting. Hirshleifer, Chordia, and Lim (2001) provide a scenario that motivates this assumption in the specific context of information collection effort. 12

15 that full observability of strategy effort a is not necessary for our results. Our predictions remain unaffected as long as the principal observes some noisy signal for a, and there is some positive correlation between how much the principal relies on the signal s and the amount of strategy effort exerted by the agent. 3 Two-period contracting 3.1 Second-period contract Using backward induction, we start with the second-period contract. At the beginning of the second period after y 1, s and a are observed, the principal chooses α 2 and β 2 to maximize the expected profit subject to the agent s participation constraint (IR) and incentive compatible constraint (IC): max α 2,β 2 E(y 2 w 2 (α 2,β 2 ) s, y 1 ) s.t. E(w 2 s, y 1 ) c(e 2 ) r 2 Var(w 2 s, y 1 ) U 2 = b TS 2, (IR) e 2 arg max e 2 E(w 2 s, y 1 ) c(e 2 ) r 2 Var(w 2 s, y 1 ). (IC) Note that the agent chooses only production effort in period two. Lemma 2 below summarizes the solution to the principal s second-period problem. Lemma 2 The optimal second-period compensation to the agent is as follows: w 2 = bkρ b θ + β 2 [y 2 E (y 2 s, y 1 )] + bv 2 + r 2 Var(w 2 s, y 1 )+c(e 2), (6) where b θ E(θ s, y 1 ) is the market s perception of the agent s ability after observing s and y 1, β 1 2 = 1+rV ar( y 2 k s,y 1 ) is the optimal pay-for-performance sensitivity for period two, e 2 = kβ 2 is k the agent s optimal effort choice, and V 2 = 2 2[1+rV ar( y 2 is the contracting surplus from the k s,y 1 )] principal-agent relationship. Further, the marginal effect of information effort a on V 2 is positive and is increasing in k (i.e., V 2 > 0 and 2 V 2 k > 0). The proof for Lemma 2 follows standard procedures and is delegated to the Appendix (A2). Lemma2offers two insights: The first is the decomposition of the second period contact in the form 13

16 of (6). Each term in (6) captures a different source of the agent s future compensation. The first term (bkρ b θ) represents the compensation for the agent s perceived ability, that is, the agent receives ashare(b) of the surplus that is attributed to his ability. The second term (β 2 [y 2 E (y 2 s, y 1 )]) is the agent s payment that is explicitly tied to his performance in excess of the benchmark E(y 2 s, y 1 ). It reflects the fact that an optimal contract filters out the randomness unrelated to the agent s effort. Thethirdtermistheagent sshare(b) of the second-period contracting surplus (V 2 ). The final two terms are compensations for the agent s risk premium and his cost of effort. ThesecondinsightfromLemma2isthatinformationeffort (a) increases the second-period contracting surplus (V 2 ). The intuition for this result is that higher a makes signal s more informative about the underlying profitability (π 1, and hence π 2 by its correlation with π 1 ). A more informative s helps the principal filter out non-effort related noise in the second-period output y 2. This reduces the conditional risk premium required by the agent and benefits the firm. The benefits are higher when the firm s growth potential becomes larger (i.e., higher k). 3.2 First-period contract Back to the first period, the agent chooses production effort (e 1 ) and information effort (a) to maximize his expected total utility, taking into account their impact on his compensations in both periods (w 1 and w 2, as in (5) and (6), respectively): 20 max e 1,a h E 0 (w 1 ) c (e 1 ) g (a) r i h 2 Var 0 (w 1 ) + E 0 (w 2 ) r i 2 Var 0 (w 2 ) c (e 2). Omitting terms unrelated to the agent s choice variables, we can rewrite the agent s objective function as (see the Appendix (A3) for detailed derivation). ³ max U 0 = E 0 (w 1 ) c(e 1 )+kρ (b β e 1,a 2 ) E 0 bθ r 2 Var 0 (w 1 )+bv 2 (a) g (a) r 2 Var 0 [E (w 2 s, y 1 )]. (7) 20 In writing the agent s objective function this way, we have utilized Lemma 1 which shows that if the agent s reported information collection effort level ea is only used for the first-period contracting in the form of (5), the agent will report truthfully. 14

17 Notice that the last four terms in (7) do not appear in the agents objective function in prior studies (such as GM, Meyer and Vickers (1997) and Indjejikian and Nanda (1999)). This is because the agents in their models do not perform strategy effort and therefore cannot affect the variability of their own compensations. Our main goal is to analyze the relation between the optimal pay-for-performance sensitivity in period one (β 1 ) and the degree of the agent s career concerns (ρ). We start by examining β 1 and ρ 0 seffects on the agent s (production and information) effort choices. First, we note that they both tend to increase the agent s production effort,as shown in prior studies. It can be easily verified from the agent s first-order condition with respect to e 1 : ³ E 0 bθ c 0 (e 1 )=β 1 + kρ (b β 2 ) = β e 1 + ρkh y (b β 2 ), (8) 1 where h y is the relative precision of the first-period output y 1 (see equation (14) in the Appendix (A2)). Equation (8) indicates that higher explicit incentive (β 1 ) leads to higher production effort. Higher reputation concerns (ρ) havethesameeffect if b β 2 > 0. To maintain the standard notion of career concerns, we restrict our discussions to the case where b β 2 > 0 because this is a necessary condition for reputation concerns to be positive (that is, for the agent to have incentive to strive for a higher, rather than lower, reputation.) 21 higher ρ implies that a lower β 1 is needed to induce the same effort e 1. behind the standard substitution effect analyzed in prior literature. When reputation concerns are present, a This is the main intuition Next, we examine the effects of β 1 and ρ on the agent s information effort a. In parallel to (8), the agent s first-order condition with respect to information effort a is: ³ bθ g 0 (a) = r V ar 0 (w 1 ) 2 {z } A>0 +[ r V ar 2 b2ρ 2 k 2 0 ] {z } B<0 + b V 2 {z } C>0 + D, (9) 21 GM and most other models assume b =1, therefore, b>β 2 by assumption. If 0 <b<β 2, then the rachet effect (i.e., too high a first-period performance raises the benchmark to which the agent s second-period performance will be compared, thus reducing the agent s incentive to work hard in the first period) dominates the reputation effect and the net dynamic incentive becomes negative. See Meyer and Vickers (1997) for an elaboration on this point. 15

18 h i where D = (b β 2 ) h y h y β 2 ρk (e 1 be 1 ). 22 The relation between β 1 on a is positive and is shown in the following lemma (the proof is in the Appendix (A4)). Lemma 3 The agent s incentive for information effort a is increasing in his explicit incentive (β 1 ). The intuition behind Lemma 3 is as follows. Higher a improves the informativeness of the signal s, thus helping filter out non-output related noise in the agent s performance measure. The agent is averse towards his current compensation risk (recall Var 0 (w 1 ) appears as a cost in the agent s objective function). Thus, the agent s incentive for effort a is higher when the marginal effect of a on Var 0 (w 1 ) is higher. Since this marginal effect is increasing in β 1 (note V ar 0(w 1 ) is higher in absolute term when β 1 is higher), the agent s incentive for a is higher when β 1 is higher. Lemma3impliesthatβ 1 carries a dual role of providing explicit incentives for both production and information effort. Whenever information effort a is more valuable, the principal could set a higher β 1 to induce a higher a. However, theeffects of ρ on information effort are more complicated, as we discuss next. The effects of ρ on information effort are captured in terms B and C in (9). Term B shows that the agent s career concerns dampen his incentive for information effort. This is a key new insight from our model. Term B is the marginal effect of information effort on the ex ante variance of the agent s future compensation ( V ar 0[E(w 2 s,y 1 )] ). The Appendix (A5) shows that V ar 0[E(w 2 s,y 1 )] is positive, and larger in magnitude when ρ is higher. That is, higher information effort is costly to the agent because it increases the agent s future compensation risk, more so when ρ is higher. This is because higher a increases the informativeness of signal s about profitability π 1 (hence the agent s ability θ). Consequently, the posterior estimate of θ (based on s) is more likely to deviate from the prior, increasing the uncertainty about the agent s future reputation, and therefore, increasing the uncertainty of his future compensation. 23 At the same time, higher a does not increase the expected 22 Note that in equilibrium, e 1 = be 1, term D disappears and does not affect the agent s choice of a. 23 This follows from the variance identity: Var(E(θ s)) = Var(θ) E(Var(θ s)). We know that more informative s reduces the ex post conditional variance Var(θ s). Thus, holding Var(θ) constant, Var(E(θ s)) will be higher, that is, the manager s ex ante uncertainty about what the market will think of him is higher. 16

19 level of the agent s reputation (i.e., E 0 [E (θ s)] = E 0 (θ) by the law of iterated expectation). result, the agent s career-risk concerns discourage information effort, 24 and more so when ρ is high. This effect works to reduce the supply of information effort from the agent, hence calls for higher explicit incentive for a. Term C in (9) indicates that the second-period contracting surplus (V 2 )providessomeincentive for the agent to exert information effort (recall that Lemma 2 shows V 2 b is positive). As a > 0 and the agent s share When ρ is high, information effort becomes more useful to improve future surplus. However, this benefit of a is not fully internalized by the agent because he obtains only b < 1 share of the future surplus. As a result, he is likely to under-supply information effort, more so when his share of the surplus b is smaller. This also calls for higher explicit incentive for information effort. In summary, the agent s career concerns as measured by ρ have two opposing effects on the agent s behaviors, and consequently, two opposing effects on the principal s optimal β 1 choice. On the one hand, higher ρ provides stronger incentive (via reputation concerns) for the agent to exert production effort e 1. as in GM. for information effort. This effect tends to lower the optimal β 1, the standard substitution effect On the other hand, higher ρ makes it more important to provide strong incentive The reasons, as described above, are that higher ρ reduces the agent s incentive to supply information effort (via career-risk concerns), and at the same time, increases the demand for information effort on the principal s side. This effect may lead to a higher β 1. These twoopposingeffects make the relation between β 1 and ρ ambiguous. formalizes this relation. The proof is in the Appendix (A6). The following proposition Proposition 1 Let β 1 be the optimal incentive β 1 for the principal. The substitutability of explicit and implicit incentives is weaker with the presence of career-risk concerns, and more so when the ³ dβ growth potential (k) is higher (i.e., 1 dρ / k > 0). Further, β 1 is increasing in ρ (i.e., dβ 1 dρ > 0, or the substitutive relation between implicit and explicit incentive is reversed), when k is sufficiently large. The intuition for Proposition 1 is as follows. We have shown that higher β 1 increases both 24 This effect is similar to Goldman (2004) where a manager is reluctant to make an investment that makes stock price more informative about his performance. 17

20 information effort a and production effort e 1 ( β 1 > 0 and e 1 β 1 production effort but decreases information effort ( e 1 > 0), while higher ρ increases > 0 and < 0). When k is low, information effort is not very important. Therefore, as ρ increases, β 1 can be lowered to induce the same level of production effort. When k is high, in contrast, information effort is relatively more important. As a result, when ρ is higher, β 1 needs to increase to induce the optimal level of information effort a. When k is sufficiently high, this positive effect may dominate the substitution effect between β 1 and ρ. The next Proposition establishes how, in the presence of career-risk concerns, β 1 relates to another parameter of interest, σ 2 θ. and the firm s profitability. decreasing in σ 2 θ for two reasons. First σ2 θ measures the ex ante uncertainty about the agent s ability When the agent cannot choose strategy effort a, theoptimalβ 1 is is the standard risk-incentive trade-off story: high σ2 θ increases the risk premium that the agent demands for accepting a contract based on stochastic output, thus lowers the optimal β 1. The second reason is that σ 2 θ increases the implicit incentive from reputation concerns (recall that E 0( b θ) e 1 is increases in σ 2 θ ), which, in turn, reduces the need for explicit incentive. When the agent chooses information effort a, σ 2 θ has two additional impacts. increase a s marginal impact on the second-period contracting surplus (i.e., increasing in σ 2 θ ). V 2 The first is to is positive and This increases the benefit of, and hence the demand for, a, whichworksto increase β 1. The second impact is to exacerbate the negative effect of career-risk concerns on the agent s information effort (recall that V ar 0( b θ) is positive and increasing in σ 2 θ ). This effect dampens the agent s incentive for, and hence reduces the supply for, a, similar to the effect of ρ as in Proposition 1. As a result, the principal may need to increase the optimal β 1. Together, when the two positive effects dominate, the optimal β 1 can be positively related to σ 2 θ. Proposition formalizes this idea. The proof is in the Appendix (A7). The next Proposition 2 Thenegativerelationbetweenrisk(σ 2 θ ) and incentive ( β 1) is weaker with the presence of career-risk concerns, and more so when the growth potential (k) and the risk level ( σ 2 θ ) are higher. Further, β 1 is increasing in σ 2 θ when k and σ2 θ are sufficiently large. 18

21 A corollary from Propositions 1 and 2 is that the positive relation between β 1 and ρ (or σ 2 θ ) is, other things equal, more likely to hold when the agent s share of the total surplus, b, is lower. This is because a lower b widens the divergence between the principal and the agent s objectives, reducing the agent s incentive to exert information effort. As a result, the principal has to impose a higher-powered incentive in period one to encourage more information effort. 3.3 Extension and sensitivity analyses Other benefits of information effort So far, our analysis has assumed that information effort a is used only for contracting purposes. We model a 0 s benefits in terms of its effect on the second-period contracting surplus V 2. However, it is more reasonable to assume that information effort has additional benefits. These benefits may stem from, for example, optimal allocation of the firm s resources or improved planning of investments in uncertain markets. As long as the marginal impact of information effort on these benefits are increasing in ρ and σ 2 θ (which is the case for V 2), 25 the results of Propositions 1 and 2 are maintained. The intuition is the following. When there are additional benefits of information effort that the agent does not fully internalize (recall that the agent only obtains b share of future surplus), there is an increased divergence between the principal and the agent regarding the optimal amount of the a effort. Given the agent s aversion to the variability in his future compensation (career-risk concerns), he will under-supply information effort. When the profitability is more persistent and when the ex ante uncertainty is higher, the signal s is more valuable. As a result, higher explicit incentive is needed to motivate more information effort. 25 These are reasonable assumptions. Denote these additional benefits as M 2 with M 2 / > 0. Intuitively, the higher the ρ, the more informative the signal s is for the second period prospects. Thus, 2 M 2 / 0 implies that the marginal benefit of information collection effort is larger when current performance signals have larger correlation with future performance. Similarly, since higher a effort reduces the uncertainty about θ, itsmarginalbenefit is likely to be non-decreasing in the level of ex ante uncertainty (i.e., 2 M 2/ σ 2 θ 0). 19

22 3.3.2 Observability of information effort We are interested in how career-risk concerns affect managers strategy effort. For career-risk concerns to arise, it is necessary to have some observability of managers strategy effort by the principal and the market. To see this point, suppose neither the principal and nor the market observes a and instead forms a belief ba based on prior information. If the belief ba does not depend on the actual a, then the ex ante uncertainty about the agent s perceived ability (Var 0 ( b θ)) is actually decreasing in a for given ba because a lowers the unconditional variance of s. As a result, there will be no career-risk concerns effect. 26 A more realistic assumption is that the principal does not directly observe a, but observes a noisy signal about a: ω = a + ε ω,whereε ω N(0, 1/p ω ). This assumption introduces uncertainty into the precision of a random variable (s), which, in general, does not allow a closed-form solution (see Subramanyam (1996) for a discussion on uncertain precision). However, our results go through under the following two conditions (details shown in the Appendix A8). The first condition is that ω does not directly depend on the realized value of s. This implies that greater information effort by the agent does not lead to a more favorable signal (it does increase the precision of the signal). This condition is necessary to preserve the linear additive structure of Bayesian updating with uncertain precision. The second condition is that the agent does not control the precision of ω (p ω ). That is, the agent has no control over how his information effort is monitored. To summarize, the mechanism of career-risk concerns does not require full observability of the agent s strategy effort a, but requires a positive link between a and the principal s assigned weight on signal s. This link builds a positive connection between a and the variability of the agent s reputation. 26 To see this, note that b θ = E(θ s, y 1, ba) = b h y (y 1 be 1)+ b h ss (here b h y and b h s are analogously defined as in (14) in the Appendix except that a is replaced by ba). Straight-forward algebra shows that holding ba constant, Var 0( b θ) is decreasing in a because a only lowers the unconditional variance of s. An equilibrium will still exist because the a effort is bounded between [0, 1] with zero (infinite) marginal cost at the low (high) end, but the result will follow the standard multi-task effort-motivation model, rather than the career-risk concerns mechanism we identify in this paper. 20